Nonlinear rapid aerodynamic modeling based on multivariate orthogonal functions

The polynomial response surface model (RSM) is a standard model in aerodynamic coefficient modeling. Real-time collected aerodynamic data are strongly correlated. Estimating the parameters of RSM by conventional least-square regression methods will yield significant errors since the regression matrix is ill-posed. A polynomial RSM based on multivariate orthogonal functions proposed here can overcome such a shortcoming and improve RSM's accuracy by iterating real-time data on the R matrix of the QR decomposed regression matrix. Moreover, RSM is further simplified by introducing Predicted Squared Error (PSE) and the R² coefficient to eliminate negligible items so that the over-fitting of the model is avoided. Part of the aerodynamic data of an F-16 wind tunnel test is interpolated with the spline function to obtain complete experimental data. The real-time data acquisition process is simulated by inputting data one by one to verify the effectiveness and real-time performance of the experimental algorithm. The multivariate orthogonal function modeling method is used to establish six models of dimensionless aerodynamic coefficients of the target aircraft, and the real-time performance of the modeling process is analyzed. Results show that the polynomial RSM based on multivariate orthogonal functions has a good predictive capability for real-time data. Meanwhile, the time consumption of each step in the modeling process is milliseconds, indicating that the method can establish the real-time modeling of the nonlinear aerodynamic coefficients of target aircraft.